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Washington State
University

Combinatorics, Linear Algebra and Number Theory Seminar

Department of Mathematics and Statistics

Meet on Zoom

https://wsu.zoom.us/j/99273222985?pwd=T3ZNR2cxZDZTWndzd2taRTZzNk5QUT09

Meeting ID: 992 7322 2985

Password: M410

April 17, Monday, 4:10 - 5:00 PM

Pan Yan

Department of Mathematics

University of Arizona

Combinatorics, Linear Algebra and Number Theory Seminar

Department of Mathematics and Statistics

Meet on Zoom

https://wsu.zoom.us/j/99273222985?pwd=T3ZNR2cxZDZTWndzd2taRTZzNk5QUT09

Meeting ID: 992 7322 2985

Password: M410

April 17, Monday, 4:10 - 5:00 PM

Pan Yan

Department of Mathematics

University of Arizona

Title: L-function for Sp(4)xGL(2) via a non-unique
model

Abstract: The theory of L-functions of automorphic forms or automorphic representations is a central topic in modern number theory. A fruitful way to study L-functions is through an integral formula, commonly referred to as an integral representation. The most common examples of Eulerian integrals are the ones which unfold to a unique model such as the Whittaker model. Integrals which unfold to non-unique models fall outside of this paradigm, and there are only a few such examples which are known to represent L-functions. In this talk, we prove a conjecture of Ginzburg and Soudry [IMRN, 2020] on an integral representation for the tensor product partial L-function for Sp(4)×GL(2) which is derived from the generalized doubling method of Cai, Friedberg, Ginzburg, and Kaplan. We show that the integral unfolds to a non-unique model and analyze it using the New Way method of Piatetski-Shapiro and Rallis.

Abstract: The theory of L-functions of automorphic forms or automorphic representations is a central topic in modern number theory. A fruitful way to study L-functions is through an integral formula, commonly referred to as an integral representation. The most common examples of Eulerian integrals are the ones which unfold to a unique model such as the Whittaker model. Integrals which unfold to non-unique models fall outside of this paradigm, and there are only a few such examples which are known to represent L-functions. In this talk, we prove a conjecture of Ginzburg and Soudry [IMRN, 2020] on an integral representation for the tensor product partial L-function for Sp(4)×GL(2) which is derived from the generalized doubling method of Cai, Friedberg, Ginzburg, and Kaplan. We show that the integral unfolds to a non-unique model and analyze it using the New Way method of Piatetski-Shapiro and Rallis.